$\dfrac{ -10g - 3h }{ -7 } = \dfrac{ 6g + 3i }{ -9 }$ Solve for $g$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ -10g - 3h }{ -{7} } = \dfrac{ 6g + 3i }{ -9 }$ $-{7} \cdot \dfrac{ -10g - 3h }{ -{7} } = -{7} \cdot \dfrac{ 6g + 3i }{ -9 }$ $-10g - 3h = -{7} \cdot \dfrac { 6g + 3i }{ -9 }$ Multiply both sides by the right denominator. $-10g - 3h = -7 \cdot \dfrac{ 6g + 3i }{ -{9} }$ $-{9} \cdot \left( -10g - 3h \right) = -{9} \cdot -7 \cdot \dfrac{ 6g + 3i }{ -{9} }$ $-{9} \cdot \left( -10g - 3h \right) = -7 \cdot \left( 6g + 3i \right)$ Distribute both sides $-{9} \cdot \left( -10g - 3h \right) = -{7} \cdot \left( 6g + 3i \right)$ ${90}g + {27}h = -{42}g - {21}i$ Combine $g$ terms on the left. ${90g} + 27h = -{42g} - 21i$ ${132g} + 27h = -21i$ Move the $h$ term to the right. $132g + {27h} = -21i$ $132g = -21i - {27h}$ Isolate $g$ by dividing both sides by its coefficient. ${132}g = -21i - 27h$ $g = \dfrac{ -21i - 27h }{ {132} }$ All of these terms are divisible by $3$ $g = \dfrac{ -{7}i - {9}h }{ {44} }$